Logic shared between many objects
The logic bricks are never shared. 

The BGE is not designed to do that (unfortunately). 

In your situation it is not a big deal. 

Equal objects

You can get equal objects (inclusive the same logic), by creating a group (with the sphere). Place the group object in another layer, scene or blend file. 

Then create instances of the group within your level scene. Instances share everything of the group object. This includes logic.

Dynamically created

Place an instance at a hidden layer. Dynamically add copies of that instance via Edit Object Actuator (Add mode) or via Python. 

This will even work in conjunction with already placed instances.

Dynamically created copies.

Place the sphere with logic at a hidden layer. Dynamically add copies of that object via Edit Object Actuator (Add mode) or via Python.